New applications of a kind of infinitesimal-operator Lie algebra (Q310436)

Summary: Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. A corresponding discrete equation approximating it is given as well. Finally, we make use of the Lie algebras to generate some new integrable systems including \((1+1)\) and \((2+1)\) dimensions.